This paper aims at presenting our algorithm used to make submission for the NIST 2013-2014 speaker recognition i-vector challenge. The fixed dimensional i-vector representation of speech utterances has attracted attentions from other communities. This challenge focuses on the task of speaker detection using i-vectors derived from conversational telephony speech data. However, the unlabeled i-vectors provided for development purpose make the problem more challenging. The proposed method uses the idea of one of the popular robust beamforming techniques named Linearly Constrained Minimum Variance (LCMV), which has been presented in the context of beamforming for signal enhancement. We will show that LCMV can improve performance by building a model from different i-vectors of a given speaker so as to cancel inter-session variability and increase inter-speaker variability. Imposter covariance matrix modification and score normalization using a selection of imposter speakers have been proposed to improve performance. As measured by minimum decision cost function defined in the challenge, our result is 27% better relative to the baseline system.